Question: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 75}{x - 9} = \dfrac{156}{x - 9}$
Explanation: Multiply both sides by $x - 9$ $ \dfrac{x^2 + 75}{x - 9} (x - 9) = \dfrac{156}{x - 9} (x - 9)$ $ x^2 + 75 = 156$ Subtract $156$ from both sides: $ x^2 + 75 - (156) = 156 - (156)$ $ x^2 + 75 - 156 = 0$ $ x^2 - 81 = 0$ Factor the expression: $ (x + 9)(x - 9) = 0$ Therefore $x = -9$ or $x = 9$ However, the original expression is undefined when $x = 9$. Therefore, the only solution is $x = -9$.